Problem: What do the following two equations represent? $3x+2y = 1$ $15x+10y = 5$
Solution: Putting the first equation in $y = mx + b$ form gives: $3x+2y = 1$ $2y = -3x+1$ $y = -\dfrac{3}{2}x + \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $15x+10y = 5$ $10y = -15x+5$ $y = -\dfrac{3}{2}x + \dfrac{1}{2}$ The above equations turn into the same equation, so they represent equal lines.